The problem of predicting selective transport of ions through nano-pores from their structure in the biological and nano-technological systems is addressed. We use a molecular dynamics simulation to provide insight into the key physical parameters of nano-pores and develop a self-consistent analytic theory describing ionic conduction and selectivity through these devices. We analyse the ion's dehydration and excess chemical potential, derive an expression for the conductivity of the nano-pore, and emphasize the role of fluctuations in its performance. The theory is verified by comparison of the predicted current-voltage characteristics with the molecular dynamics results and experimental data obtained for a graphene nano-pore and the KcsA biological channel.